Design and optimization of a compact beam-based auxiliary device for passive and adaptive vibration controls

Student thesis: PhD


The single-degree-of freedom(SDOF)mass-spring-damper is an auxiliary device commonly used for passive vibration control of structures and machineries. A wealth of studies based on this classic auxiliary device have paved the way for suppressing the unwanted vibration in structure which is subject to different types of loads. Despite the undeniable contribution to vibration control by the SDOF mass-spring-damper device, there are several inherent drawbacks, among which a frequently mentioned one is that it requires three discrete components i.e., the spring, the mass and the damping elements, thus adding to the maintenance and design cost as well as being space-consuming. In view of the above-mentioned reasons, a beam-based auxiliary device using a uniform beam to provide continuous mass, spring with or without damping elements is proposed. Many complex structures in practice grossly move like a beam, especially in low-frequency vibration. It is found in some literature about using a beam to work either as the stiffness element or the mass element in a discrete type SDOF dynamic vibration absorber (DVA). However, there is no research paper found in literature about the use of a beam structure alone as a compact vibration absorber.
In this thesis, a compact beam-based auxiliary device is proposed. The device is found to have overcome several drawbacks of the traditional discrete type mass-spring-damper when working as a SDOF dynamic vibration absorber or working in a multiple tuned mass dampers (MTMD) or as an adaptively tuned vibration absorber (ATVA) for vibration control.
It is known that when an auxiliary device acting as a DVA for weakening the contribution of a single vibration mode of a primary structure over a frequency band centered by the mode, its optimum vibration suppression performance depends solely on the mass ratio. On the other hand, the proposed beam-based DVA shows more flexibility in vibration control design due to its geometry and such physical characteristics as flexural rigidity and length. With proper design, the beam-based DVA’s vibration suppression capability can outperform that of the traditional DVA under the same mass constraint.
When the classical MTMD comprising the individual DVA is designed to increase the bandwidth and robustness of the single DVA, it always becomes space-consuming, and usually requires large attachment surface of the primary structure. The proposed compact beam-based MTMD used in this study not only overcomes to some degree of the above inconvenience caused by the classic MTMD, but also achieve comparable performance to that of the classic MTMD. A specific configuration of the classic DVA is studied first and the relevant conclusions are applied to the beam-based MTMD by approximating the impedances of the two kinds of the MTMD.
The classical ATVA is designed for suppressing a primary structure’s vibration under harmonic excitation with varying frequency. This research study proposed a beam-based ATVA, which is connected to the end of a primary cantilevered beam. It is found that adaptive vibration control at the connection point could be achieved by varying the angle between the beam-based ATVA and the primary beam. The common way of designing ATVA usually requires a variable stiffness element, generated by certain physical mechanism, to achieve a wide tunable natural frequency range. The integrated control strategy is responsible for detecting the varied excitation frequency and enabling it to automatically adapt to the new excitation frequency. Hence, the realization of the ATVA requires a full understanding of the auxiliary device’s physical mechanism that determines the auxiliary device’s natural frequency. Sometimes the nonlinearity and the uncertainties from the physical system of the ATVA will add to the complexity of the control strategy. Compared to the conventional design methodology of the ATVA, the proposed adaptive control system, developed on linear control methodology, save the cost spent on the physical system that determine the natural frequency of ATVA and reduced the potential uncertainties and the nonlinearities induced by the physical system. Besides, the analytical model of the compound system can be used to accurately predict the tunable range. Generally, this research study lays the foundation for the vibration control of structures with varying frequency excitation in a more straightforward way.
Date of Award2019
Original languageEnglish
Awarding Institution
  • The Hong Kong Polytechnic University
SupervisorWai On Wong (Chief supervisor) & Li Cheng (Co-supervisor)

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